In plotting out low-level encounters at the start of a campaign (especially with new players) I prefer to create opponents who don't want to kill the PCs right away. Instead, I generally have them use nonlethal force and capture the PCs if they lose a fight. Then I provide the PCs with a potential out to escape captivity later.

I'm aware that some GMs strongly advocate against capturing PCs on the basis that players hate the feeling of helplessness that capture provides, but I haven't had bad luck with it in the past, and its useful in generating challenging encounters with much less risk of total party kill, especially at low levels where margins for error are small (I'm talking about D&D 3.5, but this generally holds true of most tactical system RPGs as well).

In the past I've used as a pretext for this opposition consisting of slavers (the PCs will bring a fine price if captured alive) and evil cultists (the Blood God demands living sacrifices on the night of the Blood Moon!) But the truth is my imagination could use some fresh input. What other generic reasons can you think of that the opposition would use nonlethal force on the PCs?

11 Answers
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Dealing with Banditry

While killing a creature means eliminating a possible future threat now, it also means eliminating a possible future revenue stream. Dead heroes don't explore the the Temple of Disgruntled Giraffes, don't find the ring of protection +1, and don't have the ring available to steal when they're dead. So, when the heroes are defeated random bad guys don't kill them. In fact, random bad guys probably won't even take all their stuff. The adventurers need that for adventuring, and the bad guys want them to adventure because that means they can rob them again. Bad guys beat heroes into unconsciousness, take cash and other easily moved items (e.g. "You can keep your artifact sword," says the bandit, "since we don't know what it does, don't have time to identify it, and couldn't find a buyer who'd take it anyway"), tie up the heroes, and return to their hideout.

Dealing with Homeland Defense

Heroes bust into the creatures' home and slaughter a dozen creatures, but then one creature with sorcerer levels casts sleep [ench] (PH 280) and all the PCs roll 1s. It's coup de grace time, right? But beyond petty (or not so petty) revenge and a few baubles the heroes possess, what do the creatures actually get from the adventurers' deaths? Ransoming them is more lucrative. Enslaving the heroes restores the manpower lost by the heroes' incursion and, as a bonus, is humiliating. Blatantly depositing them alive at the nearest town forces the PCs to explain themselves and sends a warning to future adventurers. And using them as bargaining chips in other schemes is a strategem that persists today.

Dealing with Hunger

Many monsters want to eat PCs. But while some subsist on a diet of PCs exclusively, most would be happier with a meal that wasn't quite so stabby. Adventurers should be aware of this. Carrying food, then, is a good idea, and being able to magically make food is even better. Given the choice between a spike-covered, sword-swinging, spell-slinging adventurer and a raw steak, many creatures will choose the latter.

Dealing with the Dead

Death is remarkably easy to cure in Dungeons and Dragons if it occurs at random. Intelligent creatures of all stripes should know this. High-level creatures know that not even a body part is necessary for high-level magic to bring back the dead, and that the ex-dead, once returned, are now probably in place where they can regear and gather allies to clean the clock of the creature that make them dead in the first place. Thus alive (or, better yet, with soul trapped or transformed--but that's a different issue) is better than dead because the creature knows where the living dude is but can't be sure where the ex-dead dude will turn up.

Information: Whether they have it or not the players are sought after for something Baron von Evil (or even just Johnny Law) wants to know. Granted, in D&D you can just cast Speak With Dead, but let's face it - sometimes it's not worth the follow-up.

Respectful Opposition: Not every enemy is a murderous psychopath. Some are as LG as they come and as such are prone to using subdual damage. Even if they aren't good, sometimes the opposition just needs to be disabled, not killed.

Try-Outs: The party at large is candidate for a new group, position, or quest. As such the organizers (as it were) want their contestants to live. This could even just be an Olympic style combat where it's about the technique and not the actual kill.

Outright Theft: You don't have to kill someone to take the relic they're carrying, but that pesky group of adventurers just keeps having astute watches and is moving closer to a friendly fortress. Why not just knock them senseless long enough to steal the objet d'art.

Timely Intervention: Alas it comes to this sometimes. Did that wizard just turn the river into a stampede of horses to trample the pursuers? Sweet - we had 10 HP between us. Lethal damage? Sure, but we got away.

Wyrmwood's comment below inspires me to link This Question if coming at it from the other side is helpful.

Regarding Respectful Opposition, this was historically practiced with anyone above commoner since they were a) usually worth more ransomed than dead, and b) the captor wanted to be treated that way in case they were defeated later. So that's a possibility: have the PCs come from more-than-common families.
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SevenSidedDieDec 24 '13 at 18:40

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Good responses. These could also be used for the PCs, that is, the same reasons could also prompt PCs to be less murderous.
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WyrmwoodDec 25 '13 at 0:25

Fundamentally, I can only think of a handful of motivations for why the opponents would not kill the PCs.

Ethics: They have some system of morals in which killing people without adequate reason is wrong.

Profit: They could gain more by keeping you alive (enslaving, selling, or stealing all your stuff and only giving it back if you complete some task for them that for some reason they can't do themselves, etc.)

Fear: Fear of retribution, whether it be divine, legal, or something else.

Opportunity cost: Killing you might take too much time or resources, especially if they have things they need to do (fleeing other nasties or natural disasters, or maybe they're doing something time-sensitive).

Deus ex machina: Something else intervenes, either explicitly to save the PCs or saving them by side effect.

With these in mind, here are some examples. All the answers so far have decent logical and logistical reasons for not killing the PCs. But this is a role-playing game. We can get more fanciful.

The Duke's Armistice

This principality recently underwent a bloody civil war or suffered a large-scale massacre by raiders. The local ruler has ordained that there will be no more killing except under strict conditions, such as self-defense or legal capital punishment. The Duke, while not able to ensure complete law and order, is adequately powerful and feared/loved enough to be able to enforce this particular taboo.

This land is cursed

A variation of the above. Some magical being, or haunted residue of ancient history, ensures that terrible fates befall those who murder anyone in this area. Maybe it is just a rumor, though all those who have defied it seemed to have met similar fates...

Remember what happened to your uncle?

The opponents believe in some sort of karma, or perhaps fear blood feuds initiated by your friends and relatives, and so want to avoid cosmic or personal retribution. They are content to tie you up and take all your stuff.

Late for the ceremony

The new moon happens only once every 29.5 days, folks. The opponents need to get to the jungle colonnade before the moon sets. They want you out of commission so you can't interrupt the ceremony, but slitting each of your throats and making sure you're dead is more time consuming than a mass sleep spell and one of their fancy magic nets.

Bloody weather

They are vulnerable to daylight/moonlight/snow/rain/duststorms/locusts/some other fantastical weather event. It's coming, and they have to get out of here.

I've made a huge mistake

Something possessed by one of the PCs, whether a personal physical attribute or an artifact, resonates deeply with the attackers' mythology. Once they're close enough to start looting and finishing you off, they see something that makes them think you are anointed beings, apologize profusely for the trouble, and quietly back away.

The necromancer's Finger Dolls

This one has some permanent consequences. The local necromancer pays generously for the fingers of still-living beings. She uses them to construct some kind voodoo dolls or golems perhaps, and the magic only works if the original owner of the finger still lives. The attackers cut the ring finger off of one hand of every PC.

This could provide for some interesting quests or after-effects in the future. Perhaps the PCs have interesting phantom sensations where their fingers used to be, which vary based on what their finger is being used for and may provide some clues down the line. Or maybe the Finger Dolls miss their owners and seek out the PCs, or vice versa.

We could go on. All of these can be remixed or elaborated upon to provide more flavor. I guess the important thing to remember is that most baddies are not totally mindless (and if they are, they might not even realize the PCs aren't dead - maybe they just walk away) and have their own motivations, customs, requirements, etc., which can be exploited to provide reasons for non-lethality. I think killing should be the exception, not the norm, and your players will get used to this.

Few altercations are aimed to kill. Most animals, and people, simply want people to go away. Bandits? They want to take your stuff and not have you come after them. Animals? Unless they're trying to eat you, most just want you to leave their territory. Bullies/Thugs? They just want you to run off so they can feel like tough guys.

"Get the hell out of here or we'll kill you!" is an easy threat to use and certainly makes sense if the players have 1-2 PCs laid out unconscious. Likewise animals might growl and circle menacingly enough folks back way - think of the angry dog down the street that only gets more aggressive if you keep approaching it's territory.

Humiliation/Intimidation

Thugs and bullies might capture you just to strip you of your gear, then send you back tied to a donkey - a nice message to everyone else - "Don't mess with us". This would be an especially useful tool if you're talking different hostile humanoid groups who have been living in proximity for a long period - you don't want to kill folks because that will stir up too much reprisal, but you DO want to let them know to stay out of your territory.

Ransom

Obvious for nobles and wealthy types, but consider the other possibilities - clerics & paladins for their religious orders? Knowledgeable wizards? Ransom doesn't necessarily have to be cash - it could be trade in rights or services. "You'll give us the potion of life extension to give to our leader". "We get full control over the Eastern Lake and the fishing rights therein." "You'll evacuate the village by the hills, that's our territory" "Return the magical urn we use for our solar celebrations." etc.

Violence is usually the means to another end of some sort. Figure out what that is, and the issue of fighting to the death happens a lot less in your games.

Policy Many groups have a strong policy of doing everything they can to take their opposition alive. This includes most groups that could be conceived of as law enforcement or security. This is depending somewhat on setting of course, but it will generally hold true in most of them including many medieval based settings.

More valuable alive than dead, at least at first This is related to CatLord's answer, but there are lots of reasons that a group might find the PCs more valuable alive than dead. This includes slavers, and interrogation as he pointed out. But monsters that like to eat humanoids might also want to keep them around fresh. Also, there is conscription (this is related to slavery of course, but a nuanced form of it). Pirate crews could and did add to their crew from their victims for instance, and captured enemy commoners were sometimes pressed into service as the front ranks.

One that he didn't mention is Ransom. Remember the phrase "a King's ransom" used to be literal. It used to be very common (and in some regions still is) to capture people to hold them for ransom at the end of the conflict. In fact, even in some real Knightly tournaments there was often little actual prize money, but plenty of opportunity to to take the opponent alive and ransom him back to his family, and there were fairly accepted amounts for this transaction depending mostly on the rank of the one being ransomed.

Poorly-armed foes like peasants might not all have weapons, so they'd be using unarmed attacks - and after the players are down, there's no profit to be had slitting their throats when you can instead get them to tell you where their money is.

The local [ruler title] is in need of assistance with [generic threat], so he sends some enforcers out to press-gang travelers into joining his army. The better the PCs fight, the more useful they are to him, so he won't want to kill them.

A cannibal tribe likes to eat their foes, but have enough of a glut of captives that they're saving the PCs for later. A hole in the ground should be fine for keeping them prisoner...

As the battle nears its end, an earthquake/flash flood/rock-slide/avalanche knocks both sides over, and forces the two groups apart. In the process, the players may take a handful of rocks to the head, but at worst they'll have a headache in the morning.

When the PCs, bloodied and bruised after a long hard dungeon crawl, walk into the Kobold trap it could have ended them. Instead they're dangling from the ceiling in a net.

As you marked this system agnostic, I'd like to put in a few points from non-D&D systems:

Availability of deadly force in general

Not every system has a multitude of deadly weapons available and not all available weapons are actually deadly. In Vampire games, automatic rifle fire is laughed off while a lighted cigarette can scare a player to death. In Sci-Fi games, maybe alien species aren't harmed by lasers and in turn only carry weapons that are deadly to them... but only tickle the PCs.

Availability of deadly force specifically

In many systems, the game world has a lot of deadly force, but it's tightly controlled. In most Cyberpunk, Shadowrun and Sci-Fi games, while weapons are a dime a dozen and the government is corrupt, there are parts of the city where Corporations patrol and carrying weapons is a way to an early grave. If your target frequents a well known night club with a weapon search at the door, you better prepare to use force that gets by the guards as harmless.

Direct cost of killing

Again, in D&D, you strike, the guy is dead. Cost is zero. In other games, this may differ. If the target is well protected, the cost of killing might not be worth it. If it requires an arcane ritual to put the player from unconscious to eternal rest, there might not be time.

Indirect cost of killing

If the original goal was to kill, the the cost was already factored in. But if having the characters unable to fight back was just a means to an end, like robbing them of their possessions, then actually delivering the killing blow might promote it to something the attacker may not want. Robbing somebody is one thing. The police may have better things to do than catch a robber. Mass murder on the open streets? The police will likely build a high profile task force to catch whoever it was. That kind of attention might not be worth it.

This strongly depends on how heroic your characters are, but their first few encounters might well be fought with fists, sticks and stones. Maybe their first quest is hustling sheep from the neighbor village, or secure the right to sell in a certain market for their guild by beating up the competition. Maybe the regulars in the tavern your heroes first meet don't like [other sentient species] or wandering adventurers.

Generally, starting with less lethal combat gives you more room to escalate and raise the stakes, it can be an opportunity to practice combat and it's rules.

From a soldier's point of view, finishing off all your defeated enemies ensures that all your future enemies will fight to the death, which is not a good thing. 'No Quarter' was rare and often unpopular with the troops; after all, you might be asking for quarter yourself next month.

Good answers, Consider also the classic "we want you to go steal X from the very dangerous temple of bad guys, so off you go or we kill the Wizards' familiar" (aka so as we say or the puppy gets it). Any other form of hostage will do. I think this forms the basis of a good many movies.

It doesn't even have to require a hostage if one of the characters has such a sense of honour that once they've agreed to perform the task in exchange for his life, they'll do it.